Conductance in Electrolytic Solutions: Electrolytes and nonelectrolytes are two types of water-soluble compounds. Electrolytes are electrovalent compounds that create ions in solution. Due to this, electrolytes conduct an electric current in the solution. Electrolytes include sodium chloride, copper (II) sulphate, and potassium nitrate.

Nonelectrolytes, on the other hand, are covalent compounds that provide neutral molecules in solution. Nonelectrolytes do not conduct electricity. Nonelectrolytes include sugar, alcohol, and glycerol. As a result of the passage of electric current through its solution, an electrolyte invariably experiences chemical decomposition. We’ll talk about conductance in electrolytic solutions in this post.

Conductance of Electrolytes

We’ve seen how electrolyte solutions conduct electric currents by allowing ions to flow between electrodes. Conductivity, or conductance, is the ability of electrolytes to conduct electric currents. Electrolytes, like metallic conductors, follow Ohm’s law. The following relation provides the current I passing through a metallic conductor according to this law.

\({\text{I}} = \frac{{\text{E}}}{{\text{R}}}\)
Where,
\({\text{E}}\) is the potential difference between two points (in volts), and \({\text{R}}\) denotes the resistance in ohms (or \(\Omega \)). A conductor’s resistance \({\text{R}}\) is proportional to its length, \({\text{l,}}\) and inversely proportional to its cross-sectional area, \({\text{A}}{\text{.}}\) That is,
\({\text{R}} \propto \frac{{\text{l}}}{{\text{A}}}\)
Or
\({\rm{R = \rho \times }}\frac{{\rm{l}}}{{\rm{A}}}\)……(1)
Where,
\({\rm{\rho }}\) “rho” is a proportionality constant known as resistivity or specific resistance. Its value is determined by the conductor’s material. We can write from \(\left( 1 \right)\):
\({\rm{\rho = R \times }}\frac{{\rm{A}}}{{\rm{l}}}\)
If \({\text{l=1 cm}}\) and \({\text{A=1 sq}}{\text{.cm,}}\) then:
\({\rm{\rho = R}}\)
As a result, a conductor’s specific resistance is defined as the resistance in ohms that one-centimetre cube of it provides to the passage of electricity.

Conductance

It is a measure of ease of flow of current through a conductor
It is represented by \({\text{C}}\) and is equal to the reciprocal of resistance:
i.e., \({\text{C=1/R}}\)
Unit: \({\text{oh}}{{\text{m}}^{ – 1}}\) or \({\Omega ^{ – 1}}\) or Siemens (S)

Specific Conductivity (Or Simply Conductivity)

It is self-evident that a substance with a low resistance to current flow allows more current to travel through it. Thus, conductance, or the ability of a substance to conduct electricity, is the inverse of resistance. The reciprocal of specific resistance is known as Specific conductivity or conductivity.

It is defined as the conductance of a solution of an electrolyte in a centimetre cube (cc). The specific conductivity is denoted by the symbol \({\text{k}}\) (kappa). Thus,
\({\rm{k = }}\frac{{\rm{1}}}{{\rm{\rho }}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{R}}}{\rm{ \times }}\frac{{\rm{l}}}{{\rm{A}}}\)
\(\frac{{\text{l}}}{{\text{A}}}\) nown as cell constant.

Units of Specific Conductivity

In general, conductance is measured in reciprocal ohms (r.o), \({\text{mhos,}}\) or \({\text{Oh}}{{\text{m}}^{ – 1}}.\) The following formula can be used to calculate its unit:
\({\text{k=}}\frac{1}{{\text{A}}} \times \frac{{\text{l}}}{{\text{R}}} \times \frac{{\text{l}}}{{{\text{ohm}}}} \times \frac{{{\text{cm}}}}{{{\text{c}}{{\text{m}}^2}}}\)
\({\text{oh}}{{\text{m}}^{ – 1}}{\text{c}}{{\text{m}}^{ – 1}}\)

Equivalent Conductivity

It is the conducting power of all the ions furnished by one gm equivalent of an electrolyte present in a definite volume of solution.

It is represented by \({\Lambda _{{\text{eq}}}}.\) When concentration is changed, the number of ions present in \({\text{1 cc}}\) of the solution also changes, and consequently conductivity of the solution changes.
\({\Lambda _{{\text{eq}}}} = \frac{{\text{K}}}{{{{\text{C}}_{{\text{eq}}}}}}\)
\({\text{k=}}\) Specific conductivity, \({{\text{C}}_{{\text{eq}}}} = \) Concentration of the solution in gm eq/unit volume
\({\Lambda _{{\text{eq}}}} = {\text{k }}.{{\text{V}}_{{\text{eq}}}}\)(\({{\text{V}}_{\text{m}}} = \)Volume in \({\text{cc}}\) of the solution containing one gm equivalent of electrolyte.)
\({{\text{V}}_{{\text{eq}}}} = \frac{{1000}}{{\text{N}}}\left[{{\text{N}} ={\text{Normality}}} \right]\)
\({\Lambda _{{\text{eq}}}} = {\text{K}}.\frac{{1000}}{{\text{N}}}\)
\({\text{Unit}} = {\text{oh}}{{\text{m}}^{ – 1}}{\text{c}}{{\text{m}}^2}{\text{e}}{{\text{q}}^{ – 1}}\) or \({\text{S}}\,{\text{c}}{{\text{m}}^2}{\text{e}}{{\text{q}}^{ – 1}}\)

Molar Conductivity

It is the conducting power of all the ions furnished by one mole of an electrolyte present in a definite volume of the solution.

It is represented by \({\Lambda _{\text{m}}}.\)
\({\Lambda _{\text{m}}} = \frac{{\text{k}}}{{{{\text{C}}_{\text{m}}}}}\)
\({{\text{C}}_{\text{m}}} = \) The molar concentration of the solution
\({\Lambda _{\text{m}}} ={\text{k}}.{{\text{V}}_{\text{m}}}\) (\({{\text{V}}_{\text{m}}} = \) Volume in \({\text{cc}}\) of the solution containing \(1\,{\text{mol}}\) of electrolyte.)
\({\Lambda _{\text{m}}} = {\text{k}}.\frac{{1000}}{{\text{M}}}\) (\({\text{M=}}\) Molar concentration)
\({\text{Unit}}:{\Omega ^{ – 1}}{\text{c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ – 1}}\) Or \({\text{S}}\,{\text{c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ – 1}}.\)

Relationship Between Molar Conductivity and Equivalent Conductivity

\(\frac{{{\Lambda _{\text{m}}}}}{{{\Lambda _{{\text{eq}}}}}} = \frac{{\text{k}}}{{\text{k}}} \times \frac{{1000}}{{\text{M}}} \times \frac{{\text{N}}}{{1000}} = \frac{{\text{N}}}{{\text{M}}}\)
\(\frac{{{\Lambda _{\text{m}}}}}{{{\Lambda _{{\text{eq}}}}}} = \frac{{{\text{Mass}}\,{\text{of}}\,{\text{electolyte}}/{\text{Equivalent}}\,{\text{mass}}}}{{{\text{Mass}}\,{\text{of}}\,{\text{electolyte/Molar mass}}}}\)
\(\frac{{{\Lambda _{\text{m}}}}}{{{\Lambda _{{\text{eq}}}}}} = \frac{{{\text{Molar}}\,{\text{mass}}\,}}{{{\text{Equivalent}}\,{\text{mass}}}}\)

Measurement of Electrolytic Conductivity

The conductance of a solution is the reciprocal of its resistance. Therefore electrolytic conductivity of a solution can be measured by measuring the resistance of the solution. The resistance of an electrolytic solution is measured by using a special type of cell known as Conductivity Cell and a Wheatstone Bridge.

Conductivity Cell

The glass apparatus used for measuring the resistance of a definite volume of a solution is called a conductivity cell.

It is made of Pyrex glass and is fitted with two platinum electrodes fixed at a certain distance from each other. Conductivity cells are of different types. Some commonly used conductivity cells are shown in Figure. In a conductivity cell, the distance \(\ell \) between the two electrodes and the area \({\text{A}}\) of the electrodes are fixed. Therefore, the quantity \(\ell {\rm{/A}}\) is a constant for a particular conductivity cell. This quantity is termed cell constant. Thus,
Cell Constant \(= \frac{\ell }{{\rm{A}}}\)
The unit of Cell Constant is \({\text{c}}{{\text{m}}^{ – 1}}\) or \({{\text{m}}^{ – 1}}.\)

Wheatstone Bridge

Wheatstone Bridge is an important device used for the measurement of the resistance of a wire or of an electrolytic solution. It consists of four arms having resistances \({{\text{R}}_1}{\text{,}}{{\text{R}}_2}{\text{,}}{{\text{R}}_3}\) and \({{\text{R}}_{\text{x}}}\) connected together through a galvanometer \({{\text{V}}_{\text{o}}},\) a battery \({{\text{V}}_{{\text{EX}}}},\) as shown in Figure. Resistance \({{\text{R}}_2}\) is variable, while resistance \({{\rm{R}}_{\rm{x}}}\) is an unknown, i.e., whose value is to be measured.
Resistances \({{\text{R}}_1}\) and \({{\text{R}}_3}\) are known. After completing the circuit with the help of key \({\text{K,}}\) the variable resistance \({{\text{R}}_2}\) is adjusted in such a way that a null point is obtained i.e., there is no deflection in the galvanometer. At this stage, according to the Wheatstone Bridge Principle
\(\frac{{{{\rm{R}}_1}}}{{{{\rm{R}}_{\rm{x}}}}} = \frac{{{{\rm{R}}_2}}}{{{{\rm{R}}_3}}}\) Or \({{\text{R}}_{\text{x}}}\frac{{{{\text{R}}_1}{{\text{R}}_3}}}{{{{\text{R}}_2}}}\)
Knowing the values \({{\text{R}}_1}{\text{,}}{{\text{R}}_2}\) and \({{\text{R}}_3},\) the value of unknown resistance \({{\rm{R}}_{\rm{x}}}\) can be determined.

Variation of Specific Conductivity with Concentration

Specific conductivity is the conductivity due to the ions present in \(1\,{\text{cc}}\) of the solution. Therefore, as the concentration increases, specific conductivity increases.

Variation of Molar Conductivity with Concentration for Strong Electrolytes

Molar conductivity decreases gradually with an increase in concentration. It can be explained on the basis of Figure. At low concentration \({\Lambda _{\text{m}}}\) varies linearly with \(\sqrt {\text{c}} .\) At higher concentrations, variation is not linear. As the concentration of the solution decreases, the molar conductivity of the solution of a strong electrolyte approaches a limiting value.

If the \({\Lambda _{\text{m}}}\operatorname{vs} \sqrt {\text{c}} \) is extrapolated (i.e., up to infinite dilution), a definite value of \({\Lambda _{\text{m}}}\) is obtained. The limiting value of molar conductivity when concentration approaches zero is called \({\Lambda _{\text{m}}}\) a infinite dilution i.e., \({\Lambda _{\text{m}}} = \Lambda _{\text{m}}^\infty ,\) when \({\text{c}}\) tends to zero. Hence variation of molar conductivity with concentration for a strong electrolyte is given as
\({\Lambda _{\text{m}}} = \Lambda _{\text{m}}^\infty – {\text{b}}\sqrt {\text{c}} \)
where \({\text{b}}\) is a constant
The above equation is known as Debye Huckel Onsager Equation.

Explanation: A strong electrolyte is almost completely ionized at all dilution; therefore increase in dilution does not appreciably increase the number of ions in the solution of a strong electrolyte. The slight change in the molar conductivity of strong electrolytes with a change in concentration is actually due to a change in the interionic attraction. Concentration increases, i.e., dilution decreases (strong electrolyte), the number of ions per unit volume increases because oppositely charged ions come closer and experience a greater interionic attraction. This results in a decrease in the \({\Lambda _{\text{m}}}.\) This is why the molar conductivity of a strong electrolyte solution decreases slightly with an increase in concentration.

Variation of Molar Conductivity with Concentration for Weak Electrolyte

Dissociation of a weak electrolyte in solution is much less as compared to that of a strong electrolyte, i.e., the number of ions present in the solution of a weak electrolyte is much less than that of a strong electrolyte of the same concentration.

Hence, \({\Lambda _{\text{m}}}\) for weak electrolyte \( < {\Lambda _{\text{m}}}\) for strong electrolyte at the same concentration. When the concentration is lowered, its \({\Lambda _{\text{m}}}\)increases first slowly and then sharply at a lower concentration, i.e., it is not linear. Moreover, the curve obtained in this case does not approach the \({\Lambda _{\text{m}}}\) axis when concentration tends to zero. Thus, in this case, the curve cannot be extrapolated to obtain the limiting value of \({\Lambda _{\text{m}}},\) i.e., \(\Lambda _{\text{m}}^\infty .\) Therefore, an indirect method based upon Kohlrausch’s Law is followed.
Explanation:
Weak electrolyte does not ionize much in solution at moderate concentration. Only a few molecules of a weak electrolyte undergo dissociation into ions. As the solution becomes more and more dilute, more molecules of the weak electrolyte undergo dissociation into ions resulting in an increase in the \({\Lambda _{\text{m}}}\) of the solution.

Kohlrausch’s Law

This law states that:
The molar conductivity at infinite dilution \(\left({\Lambda _{\text{m}}^\infty } \right)\) of an electrolyte is equal to the sum of ionic conductance of its cations and anions with each conductance term multiplied by the number of respective ions present in the formula unit of the electrolyte.
It is expressed as:
\(\Lambda _{\text{m}}^\infty = {\gamma _ + }\lambda _ + ^\infty + {\gamma _ – }\lambda _ – ^\infty \)
\(\lambda _ + ^\infty \) and \(\lambda _ – ^\infty = \) ionic conductance at infinite dilution.
\({\gamma _ + }\) and \({\gamma _ – } = \) number of cation and anion
\(\lambda _ + ^0 \propto {{\text{U}}_ + },\lambda _ – ^0 \propto {{\text{U}}_ – }\)
\(\lambda _ + ^0{\text{=K}}{{\text{U}}_ + },\lambda _ – ^0{\text{=K}}{{\text{U}}_ – }\)
\({\text{K=96500}}\) coulomb, \({{\text{U}}_ + } = \) ionic mobility of cation, \({{\text{U}}_ – } = \) ionic mobility of anion.
\({\text{Ionic}}\,{\text{mobility}} = \frac{{{\text{Ionic}}\,{\text{velocity}}}}{{{\text{Potential}}\,{\text{gradient}}}}\)
\( = \frac{{\text{v}}}{{{\text{dV}}/{\text{dx}}}}\)
\({\text{v=}}\) ionic velocity, \({\text{dv=}}\) potential difference,\({\text{dx=}}\) distance between electrodes

Application of Kohlrausch’s Law

Following are important applications of Kohlrausch’s Law:
(a) Determination of Molar Conductivity of a Weak Electrolyte
(b) Determination of Degree of Dissociation

Determination of Molar Conductivity of a Weak Electrolyte

\(\Lambda _{\text{m}}^\infty \) for \({\text{N}}{{\text{H}}_4}{\text{OH,}}\) if \(\Lambda _{\text{m}}^\infty \) is given for \({\text{NaCl}},{\text{N}}{{\text{H}}_4}{\text{OH}}\) and \({\text{NaOH}}\) can be calculated as below:
\(\Lambda _{{\text{m}}\,{\text{N}}{{\text{H}}_4}{\text{OH}}}^\infty = \Lambda _{{\text{m}}\,{\text{N}}{{\text{H}}_4}{\text{Cl}}}^\infty + \Lambda _{{\text{m}}\,{\text{NaOH}}}^\infty – \Lambda _{{\text{m NaCl}}}^\infty \)

Determination of Degree of Dissociation

The degree of dissociation can be calculated as follows:

Where \(\Lambda _{\rm{m}}^{\rm{c}}=\) Molar conductance at conc. \({\rm{c}},\Lambda _{\rm{m}}^{\rm{c}} = \) Molar conductance at infinite dilution.

FAQs on Conductance in Electrolytic Solutions

Q.1. What is specific conductivity?
Ans: The reciprocal of specific resistance is known as Specific conductivity or conductivity. It is defined as the conductance of an electrolyte solution in a centimetre cube \(\left({{\text{cc}}} \right).\) It is given as:
\({\text{k}} = \frac{1}{\rho } = \frac{1}{{\text{R}}} \times \frac{l}{{\text{A}}}\)

Q.2. What is equivalent conductance?
Ans: It is the conducting power of all the ions furnished by one gm equivalent of an electrolyte present in a definite volume of solution. It is represented by \({\Lambda _{{\text{eq}}}}.\) It is given as:
\({\Lambda _{{\text{eq}}}} = {\text{k}}.\frac{{1000}}{{\text{N}}}\)

Q.3. What is molar conductivity?
Ans: It is the conducting power of all the ions furnished by one mole of an electrolyte present in a definite volume of the solution.
It is represented by \({\Lambda _{\text{m}}}.\)
\({\Lambda _{\text{m}}} = \frac{{\text{k}}}{{{{\text{C}}_{\text{m}}}}}\)
\({{\text{C}}_{\text{m}}} = \) The molar concentration of the solution
\({\Lambda _{\text{m}}} = {\text{k}}.{{\text{V}}_{\text{m}}}\) (\({{\text{V}}_{\text{m}}} = \) Volume in \({\text{cc}}\) of the solution containing \({\text{1 mol}}\) of electrolyte.)
\({\Lambda _{\text{m}}} = {\text{k}}.\frac{{1000}}{{\text{M}}}\)

4. Describe Kohlrausch’s Law.
Ans: This law states that: The molar conductivity at infinite dilution \(\left({\Lambda _{\text{m}}^\infty } \right)\) of an electrolyte is equal to the sum of ionic conductance of its cations and anions with each conductance term multiplied by the number of respective ions present in the formula unit of the electrolyte.
It is expressed as:
\(\Lambda _{\text{m}}^\infty = {\gamma _ + }\lambda _ + ^\infty + {\gamma _ – }\lambda _ – ^\infty \)
\(\lambda _ + ^\infty \) and \(\lambda _ – ^\infty = \) ionic conductance at infinite dilution.
\({\gamma _ + }\) and \({\gamma _ – } = \) number of cation and anion

Q.5. What is the application of Kohlrausch’s Law?
Ans: Following are important applications of Kohlrausch’s Law:
(a) Determination of Molar Conductivity of a Weak Electrolyte
(b) Determination of Degree of Dissociation